Cantilevered roof section

ABSTRACT

A prefabricatable structural element particularly suitable for use as a cantilevered roof structure capable of spanning large areas and including an elongated curved, preferably hyperbolicparaboloidal, surface member extending between a linear tension member and a linear compression member not sharing a plane common to the tension member. A tensioned flexible member such as a cable connected at one end thereof to a longitudinally spaced portion of the compression member engages the hyperbolicparaboloidal surface member at a plurality of predetermined locations intermediate the said tension and compression members. The tensioned flexible cable member conforms at least partly to the curvature of said surface member and cooperates with the surface member and with the linear tension and compression members so as to provide control over the deflection and flutter characteristics of the structure.

07-13-71 XR 395910991 BEST United States Patent 13,591,991

[72] Inventor Lev Zetlln 3,266,201 8/1966 Christ-.laner 52/73 X 89 Hamllton Drive, Roslyn, N.Y. 11576 3,280,518 10/l966 White 52/80 1 pp 834,101 Primary Examiner-Frank L. Abbott [22] Filed June 17, 196 Assistant Examiner-Sam D. Burke, ill [45] Patented July I3, 1971 Anaruey-Henfl Stemberg [54] g gg r fizi ABSTRACT: A prefabricatable structural element particularly suitable for use as a cantilevered roof structure capable [52] U.S.Cl. 52/73, of spanning large areas and including an elongated curved 52/18, 52/80, 52/83, 52/222 preferably hyperbolic-paraboloidal, surface member extend- 1 II- ing between a near tension member and a linear compression 504! 1/34, 1504b 7/ 14 member not sharing a plane common to the tension member. [50] Field of Search 52/80, 81, A tension/3d fl ibl member such as 3 m connected at one 83, 73 end thereof to a longitudinally spaced portion of the compression member engages the hyperbolic-paraboloidal surface Remus cued member at a plurality of predetermined locations intermediate NITE STATES PATENTS the said tension and compression members. The tensioned 1,773,656 8/1930 Wasilkowski 52/73 X flexible cable member conforms at least partly to the curva- 2,731,927 1/1956 McCain 52/83 ture of said surface member and cooperates with the surface 3,034.606 5/ 1962 Wiegand 52/83 X member and with the linear tension and compression mem- 3,090,l62 5/ 1963 Baroni..... 52/73 X bers so as to provide control over the deflection and flutter 3,195,276 7/1965 ltoh .1: sz/sox characteristics ofthe structure.

BEST AVA\LABLE COPY PATENIED Juu 3am 3.591. 991

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LEV Zeru Y BEST AVAlLABLE COPY PATENTED JUL 1 3 IBYI SHEET 3 [1F 5 CANTILEVERED ROOF SECTION STRUCTURAL ELEMENT This invention is in the field of structural elements particularly prefabricatable structural elements useful in roof and/or wall construction. More specifically this invention relates to a cantilevered hyperbolic-paraboloidal roof structure suitable for use as the covering structure for aircraft hangars, particularly hangars capable of simultaneously housing and performing maintenance on a plurality of the jumbo-sized jets, of the immediate future.

BACKGROUND OF THE INVENTION Since airports are frequently constructed on filled, or poor soil, there are usually substantial limitations on the weight of structures which may be built thereon. Severe height limitations are also imposed on airport structures because of their proximity to runways. An overall height limit of 120 feet is, for example, not unusual for a hangar facility. Nevertheless, with the advent oflarger and larger aircraft, a clear inside height of substantial dimensions must be maintained throughout the open areas of the hangar, particularly if both nosein or tail-in aircraft entry is to be permitted. A clear inside height of approximately 80 feet will, for example, be required for the Boeing 747. To permit maximum use flexibility, hangar facility should, of course, be entirely open at its periphery, since load bearing walls or columns obstruct egress and ingress of aircraft. A cantilevered roof built within the aforesaid 80-120 foot height limitations and not exceeding the pennissible weight limits would therefore be advantageous.

Since, however, the conventional truss system for roof cantilevers has already exceeded all reasonable weight limitations the conventional system being already at its maximum limits for existing sizes of aircraft it could not feasibly be used for the extra large aircraft of the future. The height and/or weight limitations of presently known roof constructions becomes prohibitive where cantilevered spans are required of such size as to be capable of simultaneously housing two airplanes of the size, for example, of the Boeing 747, particularly where overhaul and/or maintenance facilities are to be included under the same roof.

Furthermore, present day roof structures are built up vertically in layers and are therefore not readily prefabricatable since a lower layer, for example a truss assembly must be constructed before the next higher layer can be built up thereon.

It is therefore a primary object of the present invention to provide a roof structure overcoming the foregoing disadvantages.

It is another object of the present invention to provide a roof structure which has a low profile, is light in weight, economical to construct, and yet capable of spanning relatively large areas without requiring peripheral supports of any sort.

A further object of the present invention is to provide a prefabricatable structural element which may be used as a roof and/or wall element spanning large areas.

It is yet another object of the present invention to provide a roof structure of the above type which consists mainly of mass-produced elements capable of being quickly and easily assembled at the site.

A still further object of the present invention is to provide a structure having the above described characteristics and at the same time being capable of withstanding not only the static loads normally associated with large span structures but also the dynamic loads which tend to cause such structures to flutter.

A concomitant object of the present invention is to provide a structure of the above type which is readily adaptable to a variety of static and dynamic load conditions.

Large roof and/or wall structures, particularly cantilevered roof structures and particularly those spanning large areas, from time to time exhibit a motion herein referred to as EST AVAlLABLE COPY flutter." Flutter, i.e., large amplitude vibrationa. movements of, for example, the free end portion of a cantilevered structure, can result from externally applied dynamic forces such as wind and, in extreme cases, from sound waves or other sources of vibration. Thus, potentially dangerous flutter conditions can readily be induced on large-span, lightweight, cantilevered roof structures by the wind, noise and other vibrations generally prevailing at airports. Large, lightweight spans are, of course, particularly susceptible to flutter at potentially destructive levels. In accordance with the present invention, potentially dangerous flutter conditions are eliminated by the use of tensioned flexible members, such as cables, which interact with the remainder of the structure in such a manner that the entire assembly comprises an internally self dampen ing system.

According to the preferred embodiment of the present invention a roof structure comprises a plurality of novel roof sections each cantilevered from a central frame member and each including a hyperbolic-paraboloidal surface member stretched between a linear tension member and a linear compression member which is substantially coextensive with the tension member but does not share a plane in common with the latter. Elongated flexible tension members such as cables, chains or flexible tie rods, are tensioned between and connect portions of one of the linear members with longitudinally spaced portions of the other of the linear members while engaging portions of the hyperbolic-paraboloidal surface means at locations intermediate said linear tension and said linear compression members.

In its preferred fonn, the structure comprises a series of side-by-side arranged, low profile," lightweight, modular assemblies cantilevered from a central spine, or frame. Each such modular assembly includes a pair of roof sections having hyperbolic-paraboloid sheet steel surface members, linear tension and compression members in the form of, for example, I- beams, and suitably tensioned steel cables which simultaneously add strength to the structure and control flutter.

By varying the number of cables used within the structure, the locations of these cables, and the amount of tension applied to each, the same basic structural system can be readily adapted to a variety of static and dynamic load conditions.

The roof structure according to the present invention thus achieves a complete absence of flutter and a high degree of rigidity while being much lighter in weight than conventional structures of similar capabilities.

While the specification concludes with claims particularly pointing out and distinctly claiming the subject matter of this invention, it is believed that the invention will be better understood from the following description taken in connection with the accompanying drawings, in which:

FIG. 1 is a perspective diagrammatic view of an aircraft hangar installation in which a pair of roof structures according to one embodiment of the present invention are cantilevered from opposite sides of a central support;

FIG. 2 is a diagrammatic side elevational view of the hangar installation illustrated in FIG. 1;

FIG. 3 is a diagrammatic front elevational view of the hangar installation illustrated in FIGS. 1 and 2;

FIG. 4 is a diagrammatic perspective view showing in enlarged scale one embodiment of the roof assembly which is the modular building block used to build up the roof structure illustrated in FIGS. 1, 2 and 3;

FIG. 5 is a diagrammatic perspective view showing one embodiment of the interior construction, with the skin removed, of the roof assembly illustrated in FIG. 4;

FIG. 6 is a top plan view, in slightly enlarged scale, of the roof assembly illustrated in FIG. 5;

FIG. 7 is a diagrammatic perspective view of one of a plurality of roof units of progressively varying height which, according to one embodiment of the present invention, collectively fonn the roof assembly illustrated in FIGS. 5 and 6;

FIG. 8 is an enlarged sectional view taken in the direction of arrows 8-8 of FIG. 2 showing an intennediate roof assembly and portions of two adjoining roof assemblies which together form part of the roof structure illustrated in FIG. 2;

FIG. 9 is a diagrammatic perspective view of one embodiment of a cable anchoring arrangement for anchoring one end ofa cable to a valley member;

FIG. 10 is a fragmentary sectional view taken in the direction of arrows 10-10 of FIG. 9 showing, in section, a cable passing through one of the inclined bracing members illustrated in FIG. 5;

FIG. 11 is a fragmentary, partly sectional, side elevational view of a cable connection and tensioning means according to one embodiment of the present invention;

FIG. 12 is a sectional view taken in the direction of arrows 12-12 of FIG. 11;

FIG. 13 is a fragmentary, sectional view taken in the direction of arrows 13-13 of FIG. 7, showing a cable in substantially continuous engagement with the under surface of the hyperbolic-paraboloidal surface member, according to one embodiment of the present invention;

FIG, 14 is an enlarged, partly sectional, view taken in the direction of arrows 14-14 of FIG. 3 showing a portion of the central support structure and frame for cantilever-supporting the roof assemblies according to one embodiment of the present invention;

FIG. 15 is a diagrammatic side elevational view of an embodiment, according to the present invention, in which a pair of installations such as illustrated in FIG. 2 are connected edge-to-edge to form a larger installation.

The aircraft hangar installation illustrated in FIG. 1 has a double cantilevered roof construction comprising a central supporting member in the form ofa central core 1, and a pair of auxiliary supporting columns 1a and 117, at opposite sides of and cooperating with core 1, to support thereon an elongated frame 2. A pair of preferably, though not necessarily, identical roof portions 3 and 4 are secured to and cantilevered in opposite directions from the elongated frame 2. Each of the cantilevered roof portions 3 and 4 comprises a plurality of sideby-side arranged cantilevered assemblies 5.

According to the present invention, a typical assembly 5 (FIG. 4) which may be thought of as a building block or a modular element in the construction of relatively large structures such as for example the aircraft hangar roof structure illustrated in FIG. 1, comprises a rigid tension resistant ridge member 8, a pair of rigid compression resistant valley members 9 and 9, a pair of hyperbolic-paraboloidal surface members 6 and 6' which may each comprise a plurality of relatively smaller panels, e.g., panels 30, 30 of metal or strong plastic, interconnecting the valley members 9 and 9, respectively, with the ridge member 8, and preferably two pairs offlutter" cables, e.g., the cables 10, 10' and 21b, 21b interconnecting the ridge and valley members and also operatively engaging the surface members 6 and 6, respectively, at locations intermediate the ridge and valley members.

Each of the roof assemblies 5, it will be seen, is such as to form a generally rectangular outline in plan view (FIG. 6) and a generally triangular outline in elevation (FIG. 2).

While, in accordance with the preferred embodiment according to the present invention, a cantilevered construction principle is used, the stress patterns according to the present invention are different from those encountered in conventional cantilevered construction. Through the use of hyperbolic-paraboloidal surfaces, the roof structure acts as a pure shear diaphragm which has a constant stress distribution throughout. This constant stress distribution results in optimum utilization of material since all material functions at its maximum allowed stress. Because the stress is uniform, there is the additional advantage that the shell of the roof can be built up ofa plurality of prefabricated roof elements, or panels 30, each of which consists of the same structural section. Each of the prefabricated roof assemblies 5 comprises a pair of hyperbolic-paraboloidal surface members 6, 6' each formed by a plurality of the panels 30, 30' extending from opposite sides, respectively, of a central upper ridge member 8 to one BEST AVAIL4ABLE CQPY of a pair of lower valley members 9, 9'. In the cantilever arrangement according to the preferred embodiment the ridge member is a linear tension member while the valley members are linear compression members. A further advantage of the hyperbolic-paraboloidal shell structure and the cables cooperating therewith according to the present invention is the fact that any tendency of the valley compression members 9, 9 to buckle is virtually eliminated by the restraint, or lateral support, provided by. the hyperbolic-paraboloid surface member connected thereto in cooperation with said cables. As a result, the compression members may be designed at substantially their highest allowable stress as pure compression members with little or no reduction provided for buckling.

Ridge and valley members 8 and 9, which preferably comprise structural members such as steel I-beams, are disposed with respect to each other such that (1) they do not share a common plane and (2) the distance between points I: and c is less than the distance between points a and d (FIG. 4). Thus, a first portion of ridge member 8 is spaced further from the corresponding first portion of valley member 9 than a second portion of ridge member 8 is spaced from a corresponding second portion of valley member 9. A similar relationship exists between ridge member 8 and valley member 9'. It will be seen, therefore, that in the preferred embodiment each roof as sembly 5 includes a framework comprising a pair of preferably horizontal valley members 9, 9' and an inclined single ridge member 8 substantially centrally disposed preferably in a vertical plane intermediate the valley members. Each of the surface members 6, 6 together with portions of the ridge and valley members between which they extend constitute part of the respective one of the pair of surface means 7, 7. Surface means 7, for example, defined by the points a, b, c and d (FIG. 4) includes at least a longitudinally extending portion oflinear ridge member 8 and oflinear valley member 9.

The elongated flexible tension means, while preferably in the form of high strength steel cables such as flutter cables l0, 10' may also be in the form of suitable chains or suitable flexible tie rods.

The flutter cables, such as cables 10, 10', are, in accordance with the present invention, connected at their opposite ends to the ridge and to the corresponding valley member and engage portions of the corresponding surface means 7, 7' intermediate the ridge and the valley members. Each of the cables 10, 10 is arranged to engage the corresponding surface means at least at three spaced points thereon intermediate the ridge and valley member associated therewith. At least one pair of tension members, such as the cables 10, 10' extending from the apex a of the ridge member 8 down to a pair of corresponding points x and y, along valley members 9,9, respectively, longitudinally spaced from apex a, are required for purposes of this invention, The cables 10, 10 are connected to the valley members 9, 9' at points which are preferably located in the region lying between 15 to percent of the length of the respective valley members 9, 9 as measured from either of the ends thereof. Furthermore, the cables are sufiiciently flexible for each of them to conform substantially to the curvature of the corresponding surface means. The aforesaid engagement between cable and surface means may be one directly with the underside of individual ones of the panels 30 or 30 (FIG. 13) or the surface means 7, 7 may be provided with built-up portions adapted to engage the cable, or with a suitable sleeve-bearing arrangement such as illustrated in FIG. 10 with respect to the engagement between cable 10 and an inclined bracing member 12a. The engagement of the tensioned flutter cables with the surface means, 7, 7' further strengthens the roof assembly 5. These cables therefore, in addition to eliminating potentially dangerous flutter conditions of the roof structure, participate also in providing support for the structure. The extent of such participation depending upon the extent to which the cables are initially tensioned. The cables 10, 10' and, if desired, additional cables such as cables 10, 10a, and 10b, 10b, are preferably secured as illustrated in FIG. 6, interconnecting the apex a of roof as- BEST AVAILABLE COPY preferably somewhat flexible. They may be stacked and/or boxed, if desired, for easy transportation to the place of use. The panels may be serially installed between the ridge and valley members 8 and 9 in such a manner that they mutually fortify each other by being serially secured also to each other along straight linear joints 33. The slightly flexible panels become correctly undulated between their ends to collectively produce the generally hyperbolic-paraboloidal surface member 6, having straight line joints.

The panels 30 preferably are made of sheet metal such as sheet steel of suitable strength, thickness, etc. Of course, other suitable metal or plastic materials may be used. The panels may be preformed from flat generally rectangular sheets for example, with one side edge of each provided with an upward joint-forming flange 3] (FIG. 13) and the other side edge of each provided with a reversely bent flange 32, which is adapted to dovetail with the flange 31 of an adjacent panel to form a linear joint 33. Such dovetailed joints 33 may then be made secure, preferably by welding.

While, as noted, the main body of each panel between the joint portions 31 and 32 may be preliminarily flat, during installation each of the panels 30 is given a slight twist when the respective ends thereof are secured to the oppositely slanting panel-end-supporting plates 34 and 35 integral with the ridge and valley members 8 and 9, respectively (FIG. 8).

By way of example only, the surface members 6, 6' may consist of roof elements of the type known as DC decking" made by the H. H. Robertson Company, Pittsburgh, Pa. Each of the, for example, 24inch wide panels of this decking, in addition to including a jointed flat plate which forms the panel proper, includes a pair of inverted U-shaped beam sections 36 (FIG. which are integrally joined to the panel proper and extend longitudinally thereof so as to act as stiffencrs. As is well known, roofing and insulation may be placed over the inverted U-shaped beam sections after installation.

Since the panels 30 forming a surface member such as member 6, are rigidly connected to one another at their edges, and to the ridge member 8 and the corresponding valley member 9 at their ends, and cooperate with the cables as explained above, they contribute significantly to the strength of the roof assembly rather than serving merely as fill-in" or area covering" material. By permitting the interconnected panels 30 to form an integral part of the overall roof assembly, the latter becomes extremely strong considering the weight of material used therein.

A roof structure such as for example the single cantilevered roof portion 3 (FIG. I) could be built by securing ridge and valley members 9, 8, 9', 9, 8, 9 etc. in spaced relationship with each other on a frame 2 (FIG. 8) and then connecting these with panels 30, 30 so as to form the surface members 6, 6', respectively, and interconnecting these with elongated tension means such as cables 10, 10', etc. Alternate methods of construction are, however, preferred and will now be briefly described.

Preferably, a plurality of roof assemblies 5 are built and then serially lifted into position and secured to a central support frame 2 as shown in FIG. I4. Adjacent ones of these assemblies 5 are then also secured to each other along adjacent ones of their valley members. For example, the valley member 9 of one such serially arranged roof assembly 5 is connected to the valley member 9' of the next adjacent one of such serially arranged roof assemblies 5 (FIG. 8).

If, due to the size or weight thereof, or for some other reason, it is impractical to lift completely prefabricated roof assemblies 5 from ground level into position along the side edge of an elevated frame 2, then the assemblies 5 may themselves be built up of a series of smaller completely prefabricated roof units 11 (FIG. 7). In the latter eventuality. individual roof units Ila-lie, of progressively smaller average height so as to collectively form a single roof assembly 5, are assembled on the ground and sequentially lifted into place in longitudinal alignment with one another. For example, in the embodiment illustrated in FIG. 5 a set of five units Ila-11c, of varying average height, combine to form one roof assembly 5. It will be seen that each of the series of roof units Ila through 11 (FIG. 5) includes a pair of hyperbolicparaboloidal surface members 6a, 6a extending between an upper inclined chord member 8a, a pair of lower horizontal chord members 9a and 9a, opposite pairs of inclined bracing members 12a, 12a and 12b and 12b, and preferably also a pair of linear horizontal connecting members 13a and 13b (FIG. 7) connecting corresponding ends of the lower chord members 9a and 9a so as to fomi triangularly shaped end portions therewith. In addition to the cable series 10 and 21, an additional series of flexible tension means 14 may be provided for particularly large-span roof structures. Thus, a pair of flexible tension means in the form of cable members 14 and I4 are preferably, though not necessarily for purposes of this invention, provided on each of the roof units Ila-11c and extend from the apex of each such unit to the diagonally opposed lower corner of the corresponding hyperbolic-paraboloid surface member 6a, 6a. While all of the units Ila-11d (FIG. 5) have triangularly shaped end portions it will be seen that the last unit, i.e., unit ll: of each assembly 5 has, according to the preferred embodiment, only one triangular end portion, the other end portion, which forms the free end of the assembly 5, being substantially linear. In constructing an end unit such as unit lle, therefore, one pair of inclined bracing members namely members 12b and 12b may be omitted.

In following the foregoing procedure, after the roof unit He has been lifted into place, it may be secured, by suitable fastening devices to the frame 2, as illustrated in FIG. 14. Thereafter the rest of the units llb-lle are sequentially lifted into place and secured, by suitable fastening devices, to one another at adjacent triangular ends thereof, with corresponding ridge and valley members of longitudinally adjacent units in longitudinal alignment with one another.

As soon as a plurality of roof assemblies 5 have been assembled by any of the systems described above and have been connected to each other at their adjacent valley members 9, 9' (FIG. 8) any linear connecting members 13a, 13b, which were used to hold the individual assemblies together during constructing may be removed. The interaction between a plurality of adjacent cantilevered assemblies 5, connected at their adjacent valley members, is such as to provide sufficient lateral rigidity without the need for such linear connecting members, with the possible exception of the pair of assemblies 5 at the very ends of a roof structure such as structure 3.

The surface means 7 or 7 may, as noted, include bracing means such as inclined bracing members 12a, 12b etc. However, where the shell, i.e., the surface member 6 or 6 itself is sufficiently strong, the inclined bracing members 12a, 12b, etc. may not be necessary.

An example of specific dimensions and materials used in a roof embodying the present invention is a double-cantilevered roof as shown in FIG. 1 comprising two sets of each nine elongated roof assemblies of the type generally indicated at 5 in FIG. 4. Each one of the roof assemblies 5 is approximately 50 feet wide and 225 feet long. These roof assemblies are cantilevered from an elongated support frame 2 which is approximately 450 feet long. Adjacent ones of the assemblies 5 are bolted together at adjoining valley members 9, 9' (FIG. 8). The ridge member rises approximately 40 feet above the plane of the valley members, i.e., the elevation at a is 40 feet higher than at d. Since the clear inside height of the structure is approximately feet, the overall height is approximately feet.

The surface means includes IS-gauge sheet steel panels 30, each 24 inches in width and each having a pair of elongated parallel joint forming edges 31, 32 and a pair of shorter ends slightly inclined with respect to one another. Each roof assembly 5 is provided with a pair of lit-inch diameter steel cables 10, I0, and two pairs of Iii-inch diameter steel cables 10a, I0a', and 10b, 10b, respectively. The cables 14a, 14b, 14c, 14d and 142 are of l 56 inch, 1 inch, "/s inch, )6 inch and A inch diameter, respectively. Suitably dimensioned steel sembly 5 with corresponding longitudinally spaced portions of each of the valley members 9, 9'. As will be apparent to those skilled in the an, the number of such cables, their strength characteristics, and their lengths, will depend for any given roof structure, upon the size and weight of the structure and the anticipated static and dynamic loading.

It will be understood that a single pair of tension cables, e. g., cables l0, l interconnecting the apex a with longitudinally spaced locations x and y respectively on valley members 9, 9', may suffice for each roof assembly provided that the points of connection, x and y, are, as noted above, located within the range of 15-85 percent ofthe length ofsuch valley member.

As previously indicated, each roof assembly 5 also preferably includes at least one additional pair of flexible tension members such as cables 21b, 21b, etc. (FIG. 4), crossing the cables 10, respectively, connecting the fixed end portions d and d of valley members 9 and 9', respectively, with a longitudinally spaced portion, for example point m, of the ridge member 8, and engaging the corresponding surface means 7, 7' at least at three spaced points such as e.g., the points n, 0, p of surface means 7 (FIG. 5). The cables 21a, 21a serve both as flutter preventing cables and as tiedown cables for resisting upward movements of the free ends c, c of the cantilever-supported roof assembly 5 in response, for example, to upwardly directed wind forces. Similarly, an additional cable series 14 may be provided, as will be explained hereinbelow, to serve both as flutter" resisting as well as load carrying members. In other words the load, i.e., the anticipated static and dynamic loading of the roof structure is borne by the interlocked structure formed collectively by the ridge and valley members, the hyperbolic-paraboloidal surface means 7, 7 extending therebetween and connected thereto, and the flexible tensioning means l0, 10', 21a, 21a interconnecting the ridge and valley members and engaging portions of the corresponding surface means therebetween. The surface means 7, 7', the ridge and valley members 8, 9 and 9 and the tensioning means 10, 10' and 21b, 21b and, if desired, the additional tensioning means 14, 14' interacting in the noted manner, collectively form a dynamically stable roof structure.

While, in accordance with the present invention, only a single pair of cables such as 10, 10 is necessary for each roof assembly 5, nevertheless additional cables 10a, 10b and 10a, 10b, 21a, 21a, 21b, 21b etc., or some of them, may be preferred depending upon the static and anticipated dynamic loading of the structure. Continuous contact between these cables and the associated surface means 7 or 7' is preferred (FIG. 13). However, as noted above, it is sufficient if each of the aforesaid cables incorporated into the structure operatively engages the corresponding one of the surface means 7, 7 intermediate the ridge and the corresponding valley member at three spaced points along the length of such cable.

Each of the foregoing flutter cables is preferably provided, at one end thereof, with a tensioning means such as illustrated in FIG. 11. Thus, each cable, for example cable 10, may be connected by way of a suitable connector 15 to a threaded rod 16 which passes through a rigid bracket 17, shown in FIGS. 11 and 12 to be fixed to the upper ridge member 8, and provided with a suitable nut 18 on the other side thereof. The arrangement is such that in response to adjustment of nut 18 the threaded member 16 associated therewith may be drawn further through the apertured bracket 17 resulting in any desired amount of tensioning of the corresponding cable.

All of the flexible tensioning means, such as for example the cables 10, 10', substantially conform, when tensioned, to the curvature of the corresponding hyperbolic-paraboloid surface means 7, 7 so as to engage portions of the latter surface means intermediate the ridge and valley members 8, 9 and 9' respectively.

If inclined bracing members, such as members 12a, 12a, 12b. 12b, etc., are provided in the structure, they are preferably formed with suitable apertures 19 (FIG. 10). Received in each such aperture 19 is a sleeve bearing 20 BEST AVAlkABLE COPY preferably including an inner sleeve of bearing material such as, for example, Teflon, through which a corresponding one of the cables 10, etc., is adapted to slidingly pass. Relative sliding movement of the central portions of each of the cables with respect to the remainder of the roof structure is, therefore, ermitted. Thus, while opposite ends of each cable are fixed to the remainder of the roof structure, the intermediate portions of each cable are maintained, at least at three spaced location therealong, in operative engagement with, but not fixed to, the associated surface means. The operative engagement is sud! that while tension forces in the cable are transferred to the surface means, i.e., relative movement of the cable in directions generally normal to the surface of the associated surface means is restrained, relative longitudinal movement of the cable is permitted. Where inclined bracing members such as 12a are incorporated into the structure they act as stiffeners for the shell structure and form part of the surface means thereof.

A suitable anchoring device 40 (FIG. 9) may be provided at that end of each cable which is opposite the tensioning means thereof. The device 40 illustrated in FIG. 9 includes a cabh connector 41 pivotally fixed to a bracket 42 secured to a valley member 9.

Thus, flexible high-strength cables interconnect and are tensioned between the upper and lower linear cord members, i.e., ridge and valley members of the structure and the cables en gage portions of the hyperbolic-paraboloid surface means intennediate the corresponding linear ridge and valley members. if the structure is then excited by an externally applied dynamic load, the surface member, or skin, will tend to assume at any particular instant, a certain geometry. The tensioned cable, however, due to its different characteristics, wifl meanwhile tend to assume a different geometric configuration than the excited surface member. Thus, in accordance with the present invention, the cables interact with the hyperbolicparaboloidal surface means in such a way that there is always a flow of energy from the surface means, which may tend to flutter, to the cable member which is at a lower energy level. ln other words, the surface means is sufficiently dampened by its interaction with the cable system so as not to become dynamically unstable.

The cable tension may be adjusted to permit the appropriate cables to carry any desired portion of the cantilevered load as well as to provide a means for regulating the dampening effect of the cables on the remainder of the roof structure. These cables thus serve as tension members to provide control over the deflection and flutter characteristics of the roof structure.

Preferably, valley members 9, 9 of all of the roof assemblies 5 fonning the overall roof structure, lie in a common horizontal plane. Each of the elongated roof assembli s 5 is fixed at one end thereof to frame 2 by suitable structural members, such as connecting members 58, 59, 59 (H0. 14) which are part of and rigid with frame 2 and which, when secured to the respective assembly 5, form continuation: of the ridge and valley members 8, 9 and 9, respectively, of the corresponding roofassembly 5 (FIG. 14).

According to one embodiment of this invention, the surface members 6, 6 are each preferably formed by providing a plurality of elongated sheet metal panels 30, 30, respectively, of varying lengths. These panels are adapted to be readily attached to each other, edge to edge, with weatherproof, substantially straight linear joints. Only surface member 6 need be described, since surface member 6' while of opposite sense, is in all other respects identical thereto.

Similarly, all other elements denoted on the drawings by a reference numeral followed by a prime" while they may be of opposite sense, are in all other respects identical to those elements bearing the same reference numeral without the prime" designation, so that only one of each such pair of elements need be described.

The panels 30 (FIG. 4) are relatively small compared to a complete hyperbolic-paraboloidal surface member 6, and are tiedown cables 21a, 21b, 21c and 21d, positioned as shown in FIG. are also provided in interconnecting relationship with suitable steel l-beams 8, 9 and 9'.

The sizes and strengths for all of the foregoing panel and cable members will, of course, vary with the size of the structure and the static and dynamic loading anticipated. The manner of determining such sizes and strengths for a particular structure, lies within the knowledge of those skilled in the an.

The ridge and valley members, while preferably in the form of steel I-beams are not necessarily limited to such material nor to such configuration. For example, the valley members 9, 9' which are subjected to compression forces in the described roof structure, could be in the form of concrete beams or similar compression resistant members. Similarly, the ridge members which are subjected to tension forces could utilize other suitably designed rigid tension resistant members or a combination of such rigid members with one or more high strength cables or tie rods. Suitable dimensions and strength characteristics for the ridge and valley members will be readily apparent to those skilled in the art.

Similarly, the support core 1 and the columns la and lb may be of any suitable construction, well known to those skilled in the art, and one which is preferably proportioned to support the roof structure under all foreseeable load conditions including those imposed by hurricanes and earthquake forces. The frame 2 which is directly supported by core 1 and column la and lb, is also of any suitable construction adequate to cantilever-support the roof structures 3 and 4 therefrom.

While other curvatures are feasible, an advantage of the hyperbolic-paraboloidal shape of surface means 7 is that the stresses therein lie along the direction of the surface whereby the surface member itself, reinforced by the cables which cooperate therewith, assumes the various loads imposed upon the section. Thus, bending and flexural stresses are minimized, so as to eliminate the necessity for additional support members such as are presently required in conventional roof struc tures.

The effect of these stresses in the roof surface according to the preferred embodiment is to create compressive stresses in the linear valley members 9, 9' and tension stresses in the inclined ridge member 8. The many advantages of the cablereinforced hyperbolic-paraboloidal shell construction disclosed herein become quite striking in a large span roof of the type shown in FIG. 1. In this roof all of the roof assemblies 5 are supported in cantilever fashion from a single central support, namely the elongated support frame 2. Since the outside edges of the roof as a whole have no residual forces or loads to be balanced or supported by sidewalls, there is no requirement for extra supporting structures at these exterior edges.

While the structural elements according to the present invention are described in connection with a roof structure, it will be obvious that they can be used as wall and/or combined wall and roof elements.

Furthermore, it will be understood that while in its preferred form the structure according to the present invention is supported only at one end, i.e., cantilevered, at least some of its advantages will be obtained even where such structure is supported at two or more locations along its length. Thus, for example, the structure 60 illustrated in FIG. 15, supported by spaced supports 6| and 62 located along its length, is analogous to a pair of structures of the type illustrated in FIG. 2 connected to each other at their outermost edge portions. It will be noted that while-the central portion 63 of structure 60 is comprised of pairs of oppositely facing assemblies 5, of the type described above, the valley members 9, of such assemblies, because they have adjacent ends connected to each other while being supported at their spaced ends may, depending on the' loading, be in tension rather than in compression.

Also, an assembly 5 rather than being cantilevered, may itself advantageously be used with supports at both ends rather BEST AVAILABLE COPY than only at one end. Thus, for example, a roof could be constructed with one or more of the assemblies 5 supported at both ends instead of only cantilevered from one end. In the latter arrangement it will be seen that the upper (inclined) chord member is the compression member while the lower (horizontal) chord member is the tension member.

The foregoing concludes the detailed description of a particular embodiment of this invention. It will be obvious to those skilled in the art that changes and modifications may be made without departing from this invention in its broader aspects, and it is, therefore, intended in the appended claims to cover all such changes and modifications as fall within the true spirit and scope of this invention.

What I claim as new and desired to be secured by Letters Patent is:

1. A roof section adapted to be cantilevered from a support, comprising:

a first linear chord member; a second linear chord member not sharing a plane common to said first chord member, said second chord member being disposed in adjacency to said first chord member with a first portion of said second chord member spaced further from the corresponding first portion of said first chord member than a second portion of said second chord member is spaced from a cor responding second portion of said first chord member; a substantially continuous hyperbolic-paraboloidal surface means including a sheet member of resilient material extending between and connected to both said first and second linear chord members; and elongated flexible tension means interconnecting said first and second chord members and operatively engaging portions of said sheet member intermediate said first and second chord members, said elongated tension means being sufficiently flexible to conform substantially to the curvature of said surface means.

2. A roof section according to claim 1, wherein said tension means comprises a first flexible tension member connected at opposite ends thereof to said first portion of said first chord member and to said second portion of said second chord member, respectively, and a second flexible tension member connected at opposite ends thereof to said first portion of said second chord member and to said second portion of said first chord member, respectively.

3. A roof section according to claim 2 wherein said tension members are cables.

4. A roof section according to claim 3, wherein said sheet member includes a generally convex face portion and said cables are disposed adjacent to and operatively connected with said generally convex face portion.

5. A roof section according to claim 3, wherein each of said cables is operatively connected to said surface means at least at three spaced portions thereon.

6. A roof section according to claim 5, wherein said first linear chord member is a lower chord member and said second linear chord member is an upper chord member at least a major portion of which is located at a higher elevation than a corresponding portion of said lower chord member, said lower chord member being a compression-resistant member and said upper chord member being a tension-resistant member.

7. The roof section according to claim 1, wherein said surface means comprises a plurality of side-by-side arranged sheet panels, opposite ends of which are secured to said first and second linear chord members, respectively, and opposite edges of which are secured to adjacent corresponding edges of adjacent panels.

8. A roof section according to claim 1,

said surface means comprising a series of linear connecting members each joining one of a plurality of equally spaced points of said first chord member with a corresponding one of a plurality of equally spaced points of said second chord member, and said flexible tension means comprising a first series of cables joining one of said equally spaced points of said first chord member with a next adjacent one of said equally spaced point of said second chord member.

9. A roof section according to claim 8,

said flexible tension means further comprising a second series of cables each joining said first portion of said second chord member with one of a plurality of said equally spaced points of said first chord member.

10. A roof section according to claim 9,

said flexible tension means further comprising a third series of cables each joining said first portion of said first chord member to one of a plurality of spaced points of said second chord member.

11. A roof section according to claim 10, wherein at least one of said cables traverses at least one of said linear connecting members through a transverse opening provided in the latter.

12. A roof section according to claim 11,

wherein said linear connecting member is a beam and includes a sleeve means provided in said opening for slidingly receiving said one cable therein.

13. A roof section according to claim 12,

further comprising tensioning means cooperating with at least one of said cables for tensioning the latter.

14. A structure comprising in combination with a roof section according to claim 1, a support means for supporting said first portions of said first and second linear chord members so as to cantilever support said roof section.

15. A roof section according to claim 1, wherein said sheet means comprises a plurality of sheet panels with their panel ends secured to said linear chord members, respectively, and with their panel edges forming interlocking joints with the adjacent panel edges of adjacent panels, and with a plurality of said panels being intermediate panels intermediate a first end panel and a second end panel, said intermediate panels having their ends secured respectively to said first and second chord members, respectively, said first end panel having its ends secured to said first and second chord members with one of its edges secured to and forming one of said joints with one of said intermediate panels, said second end panel having its ends secured to said first and second chord members, respectively, with one of its edges secured to and forming one of said joints with another of said intermediate panels; and said tension means comprising elongated cable means interconnecting said first and second chord members and operatively engaging portions of at least three of said panels intermediate said opposite ends thereof, said cable means lying substantially adjacent to and crossing a plurality of said joints.

16. A roof structure according to claim 1 wherein said tension means are adapted to urge said portions of said sheet means in a direction to flatten said hyperbolic-paraboloidal surface means in response to tensioning of said tension means between said chord members whereby said elongated tensioning means, said surface means and said chord members cooperate to form an integrated load bearing system.

17. A roof structure according to claim 1 further comprising:

support means;

said hyperbolic-paraboloidal surface means being elongated and cantilevered at one longitudinal end thereof from said support means, said first linear chord member extending in a direction inclined with respect to the horizontal,

said elongated flexible tensioning means operatively connected at opposite end portions thereof to and tensioned between longitudinally spaced locations of said first and second linear chord members, respectively, whereby the tendency of said roof structure to flutter in response to externally applied dynamic loads is substantially reduced.

18. A roof structure according to claim 17 wherein said flexible tensioning means operatively engages said surface means at least at three predetennined spaced portions thereof.

BEST AVAILABLE COPY 19. A roof structure according to claim 17 wherein one end portion of said flexible tensioning means is operatively connected to said first linear chorttmember at a location adjacent to said support means and the other end portion of said flexible tensioning means is operatively connected to said second linear chord member at a location therealong spaced no closer to either end thereof than a distance equal to 15 percent of the length of said second linear chord member.

20. A roof structure according to claim 19, further comprising a second elongated flexible tensioning means operatively connected at one end thereof to said second linear chord member at a location adjacent said support means and the other end portion of said second tensioning means being operatively connected to a longitudinally space portion of said first linear chord member.

21. A roof structure according to claim 17 further comprising a second elongated hyperbolic-paraboloidal surface means cantilevered at one longitudinal end thereof from said support means, said second surface means including a first longitudinal edge portion extending in a direction parallel to said first linear chord member and in close adjacency thereto, a second longitudinal edge portion substantially parallel to but spaced from said second linear chord member, second elongated flexible tensioning means operatively connected at opposite end portions thereof to said first and second longitudinal edge portions respectively of said second surface means and operatively engaging predetermined portions of said second surface means intermediate said edge portions thereof, and connecting means rigidly connecting together said first linear chord member and said first longitudinal edge portion of said second surface means.

22. A roof section adapted to be cantilevered from a support, comprising:

a linear ridge means comprising an upper linear chord member lying in a substantially vertical plane and extending upwardly from a given point located in a given substantially horizontal plane;

a pair of substantially continuous hyperbolic-paraboloidal surface means including a sheet means of resilient material connected to and extending generally downwardly and outwardly from said ridge means at opposite sides thereof, respectively, and formed at the intersection thereof with said substantially horizontal plane with a pair of linear longitudinal lower edge portions at opposite sides of and substantially parallel to said substantially vertical plane; a pair of lower linear chord members located adjacent to and extending along said edge portions respectively; means securing said edge portions to said lower linear chord members, respectively, and said surface means further including a linear transverse edge portion including said given point and extending in said substantially horizontal plane transversely between the corresponding adjacent pair of ends of said pair of linear longitudinal lower edge portions, said surface means having, opposite said linear transverse edge portion, a second transverse edge portion comprising a pair of linear edge portions respectively extending downwardly and outwardly from and at opposite sides of the elevated end of said ridge means to the adjacent pair of end portions, respectively, of said longitudinal lower edge portions, whereby said roof section has a substantially rectangular projection on a horizontal plane and a substantially triangular projection on each of a pair of vertical planes respectively parallel and perpendicular to said first mentioned vertical plane; and cable means interconnecting said ridge means with each of said longitudinal lower linear chord members, respectively, and contacting said hyperbolic-paraboloidal surface means intermediate said ridge means and said lower linear chord members, respectively.

23. The roof assembly according to claim 22,

said cable means comprising a first pair of cables connected at one pair of corresponding ends thereof to the uppermost region of said'upper chord member and each connected at its opposite end to that end portion of the corresponding one of said pair of lower chord members which end portion is adjacent the lowermost region of said upper ridge member.

24. The roof assembly according to claim 23,

further comprising at least one additional pair of cables,

each connected at one end thereof to one end of a corresponding one of said lower chord members, in the region of the latter adjacent the uppermost region of said upper chord member, and each such cable connected at the opposite end thereof to said upper chord member at a region of the latter longitudinally spaced from said uppermost region.

25. A roof assembly adapted to be cantilevered from a support comprising, in combination;

a pair of spaced lower linear chord members disposed in a common substantially horizontal plane; an upper linear chord member inclined with respect to said substantially horizontal plane and disposed in a substantially vertical plane located intermediate said pair of lower chord members; a pair of continuous hyperbolic-paraboloidal surface means each including a sheet means of resilient material extending between and connected at opposite edges to said upper and to one, respectively, of said pair of lower linear chord members; and cable means connecting said upper with each of said lower linear chord members, respectively, said cable means engaging portions of said sheet means intermediate said upper and the respective one of said lower chord members.

26. A roof structure comprising a plurality of roof assemblies such as claimed in claim 25,

wherein said roof assemblies are arranged in side-by-side relationship, with lower chord members of adjacent roof assemblies being adjacent to one another, said roof structure comprising securing means for securing together said adjacent lower linear chord members of adjacent ones of said roof assemblies, and support means for fixedly sup porting corresponding end portions of each of said plurality of side-by-side secured roof assemblies at a given elevation above ground level, said plurality of roof assemblies being cantilevered from said support means.

27. A roof structure according to claim 26,

further comprising a second plurality of said side-by-side secured roof assemblies cantilevered from said support means'in direction opposite to said first plurality.

28. The roof assembly according to claim 25 wherein said cable means comprises at least one cable member, first connecting means connecting one end of said-one cable member to a given portion of said upper chord member, and second connecting means connecting the other end of said one cable member to a portion of one of said pair of lower chord members which latter portion is longitudinally spaced from said given portion of said upper chord member, one of said first and second connecting means being adjustable for varying the tension in the respective one of said cable members.

29. A roof section comprising:

BEST AVAILABLE COPY fixed support means; I m

a linear tension member cantilevered from said fixed support means;

a linear compression member fixed at one end to said support means, said compression member not sharing a plane common to said tension member but extending generally coextensive therewith and in adjacency thereto with corresponding first portions of said tension and compression members, respectively, spaced further apart than corresponding second portions of said tension and compression members;

substantially continuous hyperbolic-paraboloidal surface means including a sheet means of resilient material extending between and connected to both said tension and compression members; and

at least one elongated cable member connecting a portion of said tension member with a longitudinally spaced portion of said compression member, said cable member being located adjacent one face of said surface means and being sufficiently flexible so as to confonn substantially to the curvature of said surface means and said cable member engaging portions of said surface means intermediate said tension and said compression members so as to assist in dampening any flutter movements to which said surface means may be subjected.

30. A structural element adapted to be cantilevered from a support, comprising:

a first elongated member; a second elongated member not sharing a plane common to said first elongated member, said second member being disposed in adjacency to said first member with a first portion of said second member spaced further from the corresponding first portion of said first member than a second portion of said second member is spaced from a corresponding second portion of said first member; a substantially continuous hyperbolic-paraboloidal surface means of resilient sheet material extending between and connected to said first and second members; and elongated flexible tension means interconnecting said first and second members and operatively engaging said hyperbolic-paraboloidal surface means intermediate said first and second members, whereby said elongated tension means and said surface means cooperate to form a self dampening system.

31. A structural element according to claim 30 wherein said tension means includes adjustment means for varying the tension of said tension means, whereby the strength and flutter characteristics of said structural element may be varied.

32. A structural element according to claim 31 wherein said first and second members are linear, said tension means being connected at one end thereof to said first portion of one of said linear members and at the other end thereof to said second portion of the other of said linear members.

33. A structural element according to claim 30 wherein said tension means engages said surface means at least at three spaced locations thereon intermediate said first and second members. 

1. A roof section adapted to be cantilevered from a support, comprising: a first linear chord member; a second linear chord member not sharing a plane common to said first chord member, said second chord member being disposed in adjacency to said first chord member with a first portion of said second chord member spaced further from the corresponding first portion of said first chord member than a second portion of said second chord member is spaced from a corresponding second portion of said first chord member; a substantially continuous hyperbolicparaboloidal surface means including a sheet member of resilient material extending between and connected to both said first and second linear chord members; and elongated flexible tension means interconnecting said first and second chord members and operatively engaging portions of said sheet member intermediate said first and second chord members, said elongated tension means being sufficiently flexible to conform substantially to the curvature of said surface means.
 2. A roof section according to claim 1, wherein said tension means comprises a first flexible tension member connected at opposite ends thereof to said first portion of said first chord member and to said second portion of said second chord member, respectively, and a second flexible tension member connected at opposite ends thereof to said first portion of said second chord member and to said second portion of said first chord member, respectively.
 3. A roof section according to claim 2 wherein said tension members are cables.
 4. A roof section according to claim 3, wherein said sheet member includes a generally convex face portion and said cables are disposed adjacent to and operatively connected with said generally convex face portion.
 5. A roof section according to claim 3, wherein each of said cables is operatively connected to said surface means at least at three spaced portions thereon.
 6. A roof section according to claim 5, wherein said first linear chord member is a lower chord member and said second linear chord member is an upper chord member at least a major portion of which is located at a higher elevation than a corresponding portion of said lower chord member, said lower chord member being a compression-resistant member and said upper chord member being a tension-resistant member.
 7. The roof section according to claim 1, wherein said surface means compriSes a plurality of side-by-side arranged sheet panels, opposite ends of which are secured to said first and second linear chord members, respectively, and opposite edges of which are secured to adjacent corresponding edges of adjacent panels.
 8. A roof section according to claim 1, said surface means comprising a series of linear connecting members each joining one of a plurality of equally spaced points of said first chord member with a corresponding one of a plurality of equally spaced points of said second chord member, and said flexible tension means comprising a first series of cables joining one of said equally spaced points of said first chord member with a next adjacent one of said equally spaced point of said second chord member.
 9. A roof section according to claim 8, said flexible tension means further comprising a second series of cables each joining said first portion of said second chord member with one of a plurality of said equally spaced points of said first chord member.
 10. A roof section according to claim 9, said flexible tension means further comprising a third series of cables each joining said first portion of said first chord member to one of a plurality of spaced points of said second chord member.
 11. A roof section according to claim 10, wherein at least one of said cables traverses at least one of said linear connecting members through a transverse opening provided in the latter.
 12. A roof section according to claim 11, wherein said linear connecting member is a beam and includes a sleeve means provided in said opening for slidingly receiving said one cable therein.
 13. A roof section according to claim 12, further comprising tensioning means cooperating with at least one of said cables for tensioning the latter.
 14. A structure comprising in combination with a roof section according to claim 1, a support means for supporting said first portions of said first and second linear chord members so as to cantilever support said roof section.
 15. A roof section according to claim 1, wherein said sheet means comprises a plurality of sheet panels with their panel ends secured to said linear chord members, respectively, and with their panel edges forming interlocking joints with the adjacent panel edges of adjacent panels, and with a plurality of said panels being intermediate panels intermediate a first end panel and a second end panel, said intermediate panels having their ends secured respectively to said first and second chord members, respectively, said first end panel having its ends secured to said first and second chord members with one of its edges secured to and forming one of said joints with one of said intermediate panels, said second end panel having its ends secured to said first and second chord members, respectively, with one of its edges secured to and forming one of said joints with another of said intermediate panels; and said tension means comprising elongated cable means interconnecting said first and second chord members and operatively engaging portions of at least three of said panels intermediate said opposite ends thereof, said cable means lying substantially adjacent to and crossing a plurality of said joints.
 16. A roof structure according to claim 1 wherein said tension means are adapted to urge said portions of said sheet means in a direction to flatten said hyperbolic-paraboloidal surface means in response to tensioning of said tension means between said chord members whereby said elongated tensioning means, said surface means and said chord members cooperate to form an integrated load bearing system.
 17. A roof structure according to claim 1 further comprising: support means; said hyperbolic-paraboloidal surface means being elongated and cantilevered at one longitudinal end thereof from said support means, said first linear chord member extending in a direction inclined with respect to the horizontal, said elongated flexible tensionIng means operatively connected at opposite end portions thereof to and tensioned between longitudinally spaced locations of said first and second linear chord members, respectively, whereby the tendency of said roof structure to flutter in response to externally applied dynamic loads is substantially reduced.
 18. A roof structure according to claim 17 wherein said flexible tensioning means operatively engages said surface means at least at three predetermined spaced portions thereof.
 19. A roof structure according to claim 17 wherein one end portion of said flexible tensioning means is operatively connected to said first linear chord member at a location adjacent to said support means and the other end portion of said flexible tensioning means is operatively connected to said second linear chord member at a location therealong spaced no closer to either end thereof than a distance equal to 15 percent of the length of said second linear chord member.
 20. A roof structure according to claim 19, further comprising a second elongated flexible tensioning means operatively connected at one end thereof to said second linear chord member at a location adjacent said support means and the other end portion of said second tensioning means being operatively connected to a longitudinally space portion of said first linear chord member.
 21. A roof structure according to claim 17 further comprising a second elongated hyperbolic-paraboloidal surface means cantilevered at one longitudinal end thereof from said support means, said second surface means including a first longitudinal edge portion extending in a direction parallel to said first linear chord member and in close adjacency thereto, a second longitudinal edge portion substantially parallel to but spaced from said second linear chord member, second elongated flexible tensioning means operatively connected at opposite end portions thereof to said first and second longitudinal edge portions respectively of said second surface means and operatively engaging predetermined portions of said second surface means intermediate said edge portions thereof, and connecting means rigidly connecting together said first linear chord member and said first longitudinal edge portion of said second surface means.
 22. A roof section adapted to be cantilevered from a support, comprising: a linear ridge means comprising an upper linear chord member lying in a substantially vertical plane and extending upwardly from a given point located in a given substantially horizontal plane; a pair of substantially continuous hyperbolic-paraboloidal surface means including a sheet means of resilient material connected to and extending generally downwardly and outwardly from said ridge means at opposite sides thereof, respectively, and formed at the intersection thereof with said substantially horizontal plane with a pair of linear longitudinal lower edge portions at opposite sides of and substantially parallel to said substantially vertical plane; a pair of lower linear chord members located adjacent to and extending along said edge portions respectively; means securing said edge portions to said lower linear chord members, respectively, and said surface means further including a linear transverse edge portion including said given point and extending in said substantially horizontal plane transversely between the corresponding adjacent pair of ends of said pair of linear longitudinal lower edge portions, said surface means having, opposite said linear transverse edge portion, a second transverse edge portion comprising a pair of linear edge portions respectively extending downwardly and outwardly from and at opposite sides of the elevated end of said ridge means to the adjacent pair of end portions, respectively, of said longitudinal lower edge portions, whereby said roof section has a substantially rectangular projection on a horizontal plane and a substantially triangular projection on each of a pair of vertical planes respectivEly parallel and perpendicular to said first mentioned vertical plane; and cable means interconnecting said ridge means with each of said longitudinal lower linear chord members, respectively, and contacting said hyperbolic-paraboloidal surface means intermediate said ridge means and said lower linear chord members, respectively.
 23. The roof assembly according to claim 22, said cable means comprising a first pair of cables connected at one pair of corresponding ends thereof to the uppermost region of said upper chord member and each connected at its opposite end to that end portion of the corresponding one of said pair of lower chord members which end portion is adjacent the lowermost region of said upper ridge member.
 24. The roof assembly according to claim 23, further comprising at least one additional pair of cables, each connected at one end thereof to one end of a corresponding one of said lower chord members, in the region of the latter adjacent the uppermost region of said upper chord member, and each such cable connected at the opposite end thereof to said upper chord member at a region of the latter longitudinally spaced from said uppermost region.
 25. A roof assembly adapted to be cantilevered from a support comprising, in combination; a pair of spaced lower linear chord members disposed in a common substantially horizontal plane; an upper linear chord member inclined with respect to said substantially horizontal plane and disposed in a substantially vertical plane located intermediate said pair of lower chord members; a pair of continuous hyperbolic-paraboloidal surface means each including a sheet means of resilient material extending between and connected at opposite edges to said upper and to one, respectively, of said pair of lower linear chord members; and cable means connecting said upper with each of said lower linear chord members, respectively, said cable means engaging portions of said sheet means intermediate said upper and the respective one of said lower chord members.
 26. A roof structure comprising a plurality of roof assemblies such as claimed in claim 25, wherein said roof assemblies are arranged in side-by-side relationship, with lower chord members of adjacent roof assemblies being adjacent to one another, said roof structure comprising securing means for securing together said adjacent lower linear chord members of adjacent ones of said roof assemblies, and support means for fixedly supporting corresponding end portions of each of said plurality of side-by-side secured roof assemblies at a given elevation above ground level, said plurality of roof assemblies being cantilevered from said support means.
 27. A roof structure according to claim 26, further comprising a second plurality of said side-by-side secured roof assemblies cantilevered from said support means in direction opposite to said first plurality.
 28. The roof assembly according to claim 25 wherein said cable means comprises at least one cable member, first connecting means connecting one end of said one cable member to a given portion of said upper chord member, and second connecting means connecting the other end of said one cable member to a portion of one of said pair of lower chord members which latter portion is longitudinally spaced from said given portion of said upper chord member, one of said first and second connecting means being adjustable for varying the tension in the respective one of said cable members.
 29. A roof section comprising: fixed support means; a linear tension member cantilevered from said fixed support means; a linear compression member fixed at one end to said support means, said compression member not sharing a plane common to said tension member but extending generally coextensive therewith and in adjacency thereto with corresponding first portions of said tension and compression members, respectively, spaced further apart than corresponding second portions of said tension and compreSsion members; substantially continuous hyperbolic-paraboloidal surface means including a sheet means of resilient material extending between and connected to both said tension and compression members; and at least one elongated cable member connecting a portion of said tension member with a longitudinally spaced portion of said compression member, said cable member being located adjacent one face of said surface means and being sufficiently flexible so as to conform substantially to the curvature of said surface means and said cable member engaging portions of said surface means intermediate said tension and said compression members so as to assist in dampening any flutter movements to which said surface means may be subjected.
 30. A structural element adapted to be cantilevered from a support, comprising: a first elongated member; a second elongated member not sharing a plane common to said first elongated member, said second member being disposed in adjacency to said first member with a first portion of said second member spaced further from the corresponding first portion of said first member than a second portion of said second member is spaced from a corresponding second portion of said first member; a substantially continuous hyperbolic-paraboloidal surface means of resilient sheet material extending between and connected to said first and second members; and elongated flexible tension means interconnecting said first and second members and operatively engaging said hyperbolic-paraboloidal surface means intermediate said first and second members, whereby said elongated tension means and said surface means cooperate to form a self dampening system.
 31. A structural element according to claim 30 wherein said tension means includes adjustment means for varying the tension of said tension means, whereby the strength and flutter characteristics of said structural element may be varied.
 32. A structural element according to claim 31 wherein said first and second members are linear, said tension means being connected at one end thereof to said first portion of one of said linear members and at the other end thereof to said second portion of the other of said linear members.
 33. A structural element according to claim 30 wherein said tension means engages said surface means at least at three spaced locations thereon intermediate said first and second members. 